$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 7$ and $ BC = 6x + 8$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 7} = {6x + 8}$ Solve for $x$ $ 3x = 15$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({5}) - 7$ $ BC = 6({5}) + 8$ $ AB = 45 - 7$ $ BC = 30 + 8$ $ AB = 38$ $ BC = 38$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {38} + {38}$ $ AC = 76$